BIFURCATIONS OF THREE AND FOURDIMENSIONAL MAPS: UNIVERSAL PROPERTIES
Cite this article as:
Kuznetsov A. P., Sedova Y. V. BIFURCATIONS OF THREE AND FOURDIMENSIONAL MAPS: UNIVERSAL PROPERTIES. Izvestiya VUZ. Applied Nonlinear Dynamics, 2012, vol. 20, iss. 5, pp. 26-43. DOI: https://doi.org/10.18500/0869-6632-2012-20-5-26-43
The approach, in which the picture of bifurcations of discrete maps is considered in the space of invariants of perturbation matrix (Jacobi matrix), is extended to the case of three and four dimensions. In those cases the structure of surfaces, lines and points for bifurcations, that is universal for all maps, is revealed. We present the examples of maps, whose parameters are governed directly by invariants of the Jacobian matrix.
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BibTeX
author = {A. P. Kuznetsov and Yu. V. Sedova },
title = {BIFURCATIONS OF THREE AND FOURDIMENSIONAL MAPS: UNIVERSAL PROPERTIES},
year = {2012},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {20},number = {5},
url = {https://old-andjournal.sgu.ru/en/articles/bifurcations-of-three-and-fourdimensional-maps-universal-properties},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2012-20-5-26-43},pages = {26--43},issn = {0869-6632},
keywords = {maps,bifurcations,multiplier,perturbation matrix.},
abstract = {The approach, in which the picture of bifurcations of discrete maps is considered in the space of invariants of perturbation matrix (Jacobi matrix), is extended to the case of three and four dimensions. In those cases the structure of surfaces, lines and points for bifurcations, that is universal for all maps, is revealed. We present the examples of maps, whose parameters are governed directly by invariants of the Jacobian matrix. }}